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Hamiltonian math 
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#1
Dec912, 12:09 AM

P: 606

I'm watching a lecture on the Hamiltonian and can't figure out something. Here it is. Take a generic function G, and differentiate it with respect to p and q. What you get is the partial of G with respect to p TIMES the derivative of p (or pdot), plus the derivative of G with respect to q TIMES qdot.
My question is, where does the pdot and qdot terms come into the equation here? Why isn't it just the partial of G over p plus the partial of G over q? 


#2
Dec912, 12:30 AM

Mentor
P: 11,862

What you've described looks like taking the derivative of G(p,q) with respect to t, using the chain rule:
$$\frac{dG(p,q)}{dt} = \frac{\partial G}{\partial p} \frac{dp}{dt} + \frac{\partial G}{\partial q} \frac{dq}{dt}$$ 


#3
Dec912, 12:52 AM

P: 606

It certainly does, thanks jtbell.



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